2.4.3 Other Velocity Equations
Because of the difficulties involved in determining the shear stress and hence the velocity
distribution in turbulent flows, other approaches to determine mean velocities in rivers has been
prevalent. Two such equations are in common use. They are Manning's equation:
Ku
R 2 / 3 S1/ 2
V=
(2.83)
f
n
and Chezy's equation
V = CR1/ 2 S1/ 2
(2.84)
f
where:
V
=
Average velocity in the waterway cross-section in m/s, ft/s
n
=
Manning's roughness coefficient
R
=
Hydraulic radius in m or ft equal to the cross-sectional area A divided by the
wetted perimeter P of the waterway m, ft
=
Friction slope m/m, ft/ft
Sf
C
=
Chezy's discharge coefficient known as Chezy's C
=
1.0
(SI)
Ku
=
1.486 (English)
Ku
In these equations, the boundary shear stress is expressed implicitly in the roughness coefficient
"n" or in the discharge coefficient C. By equating the velocity determined from Manning's
equation with the velocity determined from Chezy's equation, the relation between the
coefficients is
K u 1/ 6
C=
(2.85)
R
n
If the flow is gradually varied, Manning's and Chezy's equations are used with the average
station or over a short length increment 300 m (1,000 ft ) for example at an instant of time, or
both.
Over many decades, a catalog of values of Manning's n and Chezy's C has been assembled so
that an engineer can estimate the appropriate value by knowing the general nature of the
channel boundaries. An abbreviated list of Manning's roughness coefficients is given in Table
2.1. Additional values are given by Barnes (1967) and Chow (1959). Manning's n for sandbed
and gravel-bed channels is discussed in detail in Chapter 3.
2.21
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